Integrated doppler measurement is a ranging technique used extensively in radio-navigation systems such as the global positioning system (GPS) and LORAN-C. The purpose of integrated doppler measurement is to determine line-of-sight range changes between a transmitter and receiver which are moving relative to one another. These range changes can then be used by a navigation computer to precisely determine receiver location and velocity.
Integrated doppler measurement involves the process of measuring at the receiver phase shifts in a signal received from the transmitter and converting the measured phase shifts to a change in transmitter-to-receiver range. The phase shift measurement is typically performed with the aid of a carrier tracking loop which frequency locks a signal generated within the receiver with the received signal. A carrier tracking loop is a closed loop circuit which tracks the phase of a received signal that has either a residual carrier component or a suppressed carrier component. The carrier tracking loop may be a phase-lock loop for residual carrier tracking or a Costas loop or squaring loop for suppressed carrier tracking.
FIG. 1 shows a known receiver 2 which is capable of making integrated doppler measurements. Receiver 2 has an antenna 4 for receiving a signal from a remote transmitter (not shown). The received signal is amplified by low noise amplifier 6 and down-converted by frequency down-converter 8. The output signal, y.sub.i (t), of frequency down-converter 8 is then applied to a first input of phase detector 12 of carrier tracking loop 10. Carrier tracking loop 10 is a conventional analog phase-lock loop consisting of a loop filter 14 connected to phase detector 12 and a voltage controlled oscillator (VCO) 16 connected to loop filter 14 and phase detector 12.
The output signal, y.sub.o (t), of VCO 16, which is an estimate of the received signal as output by the frequency down-converter 8, is applied to a second input of phase detector 12. Phase detector 12 produces a loop error signal, E.sub.0 (t), which is related to the phase difference between signals y.sub.i (t) and y.sub.o (t).
In the absence of noise and where the transmitted signal is sinusoidal, signals y.sub.i (t), y.sub.o (t), and E.sub.0 (t) typically have the following forms: EQU y.sub.i (t)=Bsin[.theta.(t)]; EQU y.sub.o (t)=Csin[.theta.(t)]; EQU E.sub.0 (t)=Asin[(t)-.theta.(t)]; (Eq. 1)
where B, C, and A are the maximum noiseless amplitudes of signals y.sub.i (t), y.sub.o (t), and E.sub.0 (t) , respectively, and .theta.(t) and .theta.(t) are phase processes described by phase offset, frequency, and frequency rate. The value B is maintained substantially constant by an automatic gain control circuit in frequency down-converter 8. The value C is maintained substantially constant by VCO 16. The value A is maintained substantially constant by phase detector 12 when values B and C of signals y.sub.i (t) and y.sub.o (t) are substantially constant.
The error signal E.sub.0 (t) is filtered by loop filter 14, which is typically a lead-compensated integrator, to produce a control signal which is applied to the input of VCO 16. The control signal produced by loop filter 14 causes the output signal y.sub.o (t) of VCO 16 to become synchronous with the output signal y.sub.i (t) of frequency down converter 8. When signals y.sub.i (t) and y.sub.o (t) become synchronous, that is, have the same frequency and phase, the carrier tracking loop is locked.
After carrier tracking loop 10 is locked, the value of the control signal produced by loop filter 14 is proportional to .omega..sub.D, the Doppler shift in carrier frequency (radians/second) due to the relative velocity between the receiver 2 and the transmitter (not shown). The control signal produced by loop filter 14 is applied to integrator 20 in accumulated delta range (ADR) measurement circuit 18 which performs the integrated doppler measurement.
Integrator 20 produces an output signal having a phase process, that is, phase offset, frequency, and frequency rate, which is equal to the phase process of y.sub.o (t). While carrier tracking loop 10 is locked, the output signal of integrator 20 is indicative of the instantaneous phase, .phi., of both the received signal y.sub.i (t) and the estimated signal y.sub.o (t). Sample and hold circuit 22 samples the output of integrator 20 and applies the sampled signal to a first input of sum circuit 24 in response to timing signals from timing controller 30. A second input of sum circuit 24 receives the output signal directly from integrator 20.
Sum circuit 24 determines the change in phase, .phi.(t.sub.i)-.phi.(t.sub.i-1, during a time period from time t.sub.i-1 to t.sub.i and applies a signal indicative of this value to amplifier 26. Amplifier 26 converts this phase change to the line-of-sight range change, .DELTA.R, during the time period from time t.sub.i-1 to t.sub.i, given by: EQU .DELTA.R=[.lambda./2.pi.][.phi.(t.sub.i)-.phi.(t.sub.i-1)]=R(t.sub.i)-R(t.s ub.i-1);
where:
R(t)=the line-of-sight range as a function of time; and PA1 k=Boltzman's constant; PA1 T=absolute temperature; PA1 B=bandwidth (Hz); and PA1 J=received jammer power (watts/Hz). PA1 .omega..sub.n =loop bandwidth; PA1 .omega..sub.D =a.omega..sub.c /c; PA1 a=line-of-sight acceleration between the transmitter and receiver;
.lambda.=known carrier wavelength.
Accumulator 28 sums the measurements of many small range changes, .DELTA.R's, in response to timing signals from timing controller 30, to determine the accumulated delta range, ADR, given by: ##EQU1##
The ADR value output by accumulator 28 is applied to navigation computer 32 and may be used to calculate the position and velocity of receiver 2.
The ability of receiver 2 to make accurate integrated doppler measurements is dependent on the ability of carrier tracking loop 10 to remain in lock. If carrier tracking loop 10 breaks lock, the output of loop filter 14 will no longer be proportional to the doppler frequency, .omega..sub.D. As a result, when carrier tracking loop 10 breaks lock, ADR measurement circuit 18 will be unable to accurately determine line-of-sight range changes between the transmitter and receiver 2.
As is well known, noise which is received by antenna 4 or produced by receiver 2 itself, will be 30 superimposed on the signal received from the transmitter and consequently on error signal E.sub.0 (t) produced by phase detector 12. When such noise exceeds a certain level, the carrier tracking loop begins to slip cycles, that is, periodically break lock briefly and then relock. Increasing the noise beyond this level increases the rate at which cycle slipping occurs thus increasing the amount of time that the carrier tracking loop is out of lock until eventually the carrier tracking loop is definitively out of lock and is unable to relock.
Prior attempts to limit the effect of noise on the ability of a carrier tracking loop to remain in lock have been limited to reducing the bandwidth of the loop. Reducing loop bandwidth increases the signal-to-noise ratio (SNR) in the loop since white noise power, N.sub.o, and power from "white-like" manmade interference, N.sub.j, are functions of bandwidth as given by: EQU N.sub.o =10log[kTB]; EQU N.sub.j =10log[JB];
where:
However, the relative movement between the transmitter and receiver affects the limit to which the loop bandwidth can be narrowed and still maintain carrier tracking. For a second order carrier tracking loop with an active integrator loop filter, the steady state phase error, .phi..sub.ss, is given by: EQU .phi..sub.ss =sin.sup.-1 [.omega..sub.D /.omega..sub.n.sup.2 ]; (Eq. 2)
where:
c=speed of light; and
.omega..sub.c =carrier frequency. For .vertline..phi..sub.ss .vertline..ltoreq..pi./10, .omega..sub.n=.omega..sub.D / .vertline..phi..sub.ss .vertline.and the carrier tracking loop will remain locked onto the carrier signal. If .phi..sub.ss exceeds the breaklock limit of about .pi./10 radians or 18 degrees, the loop error signal becomes nonlinear and the loop will break lock. Hence, the minimum loop bandwidth, .omega..sub.nmin, is given by: ##EQU2##
Experimental studies have shown that the minimum signal-to-noise ratio, SNR.sub.min, with which a carrier tracking loop of bandwidth .omega..sub.nmin can remain locked onto a signal having a doppler rate .omega..sub.D and white noise interference is given by: EQU SNR.sub.min =10log[.omega..sub.nmin/.sup.20.pi. ]dB. (Eq. 4)
For signal-to-noise ratios less than SNR.sub.min, a carrier tracking loop with a bandwidth of .omega..sub.nmin will break lock and accurate integrated doppler measurements will not be able to be performed.
Accordingly, in order to be able to perform accurate integrated doppler measurements in the presence of noise levels which result in a signal-to-noise ratio less than SNR.sub.min, a need exists for a carrier tracking loop which will maintain lock in the presence of such noise levels.